Interior point methods of mathematical programming:
The book provides an overview of the research in interior point methods since the publication of N. Karmarkar's seminal paper in 1984. Leading international experts have contributed to the book with summaries of their relevant areas of specialization. Part I gives an overview of basic variants...
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer Acad. Publ.
1996
|
| Series: | Applied optimization
5 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | The book provides an overview of the research in interior point methods since the publication of N. Karmarkar's seminal paper in 1984. Leading international experts have contributed to the book with summaries of their relevant areas of specialization. Part I gives an overview of basic variants of interior point algorithms for linear programming. Duality-theory for LP and sensitivity analysis is developed. Results on the affine scale, path following, potential reduction, infeasible interior point methods and implementation strategies are discussed. Part II deals with nonlinear programming. Here necessary smoothness conditions are introduced and illustrated. Algorithms for general smooth convex problems, complementarity and semidefinite optimization problems are presented. The implementation of barrier methods for general nonlinear optimization problems is also considered. Part III covers some application areas such as combinatorial optimization, global optimization and VLSI design. |
| Physical Description: | XXI, 528 S. graph. Darst. |
| ISBN: | 0792342011 |
Staff View
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| 245 | 1 | 0 | |a Interior point methods of mathematical programming |c ed. by Tamás Terlaky |
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| 490 | 1 | |a Applied optimization |v 5 | |
| 520 | 3 | |a The book provides an overview of the research in interior point methods since the publication of N. Karmarkar's seminal paper in 1984. Leading international experts have contributed to the book with summaries of their relevant areas of specialization. Part I gives an overview of basic variants of interior point algorithms for linear programming. Duality-theory for LP and sensitivity analysis is developed. Results on the affine scale, path following, potential reduction, infeasible interior point methods and implementation strategies are discussed. Part II deals with nonlinear programming. Here necessary smoothness conditions are introduced and illustrated. Algorithms for general smooth convex problems, complementarity and semidefinite optimization problems are presented. The implementation of barrier methods for general nonlinear optimization problems is also considered. Part III covers some application areas such as combinatorial optimization, global optimization and VLSI design. | |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
PREFACE xv
Part I LINEAR PROGRAMMING 1
1 INTRODUCTION TO THE THEORY OF
INTERIOR POINT METHODS
Benjamin Jansen, Cornells Roos, Tamds Terlaky 3
1.1 The Theory of Linear Programming 3
1.2 Sensitivity Analysis in Linear Programming 14
1.3 Concluding Remarks 30
REFERENCES 31
2 AFFINE SCALING ALGORITHM
Takashi Tsuchiya 35
2.1 Introduction 35
2.2 Problem and Preliminaries 38
2.3 The Affine Scaling Algorithm 40
2.4 Nondegeneracy Assumptions 47
2.5 Basic Properties of the Iterative Process 50
2.6 Global Convergence Proof Under a Nondegeneracy Assumption 54
2.7 Global Convergence Proof Without Nondegeneracy Assumptions 56
2.8 The Homogeneous Affine Scaling Algorithm 59
2.9 More on the Global Convergence Proof of the Affine Scaling
Algorithm 67
2.10 Why Two Thirds is Sharp for the Affine Scaling? 68
2.11 Superlinear Convergence of the Affine Scaling Algorithm 69
2.12 On the Counterexample of Global Convergence of The Affine
Scaling Algorithm 70
vii
2.13 Concluding Remarks 73
2.14 Appendix: How to Solve General LP Problems with the Affine
Scaling Algorithm 75
REFERENCES 77
3 TARGET FOLLOWING METHODS FOR
LINEAR PROGRAMMING
Benjamin Jansen, Cornells Roos, Tamds Terlaky 83
3.1 Introduction 83
3.2 Short step Primal dual Algorithms for LP 86
3.3 Applications 93
3.4 Concluding Remarks 121
REFERENCES 121
4 POTENTIAL REDUCTION ALGORITHMS
Kurt M. Anstreicher 125
4.1 Introduction 125
4.2 Potential Functions for Linear Programming 126
4.3 Karmarkar s Algorithm 130
4.4 The Affine Potential Reduction Algorithm 134
4.5 The Primal Dual Algorithm 139
4.6 Enhancements and Extensions 142
REFERENCES 151
5 INFEASIBLE INTERIOR POINT ALGORITHMS
Shinji Mizuno 159
5.1 Introduction 159
5.2 An IIP Algorithm Using a Path of Centers 161
5.3 Global Convergence 164
5.4 Polynomial Time Convergence 172
5.5 An IIP Algorithm Using a Surface of Centers 175
5.6 A Predictor corrector Algorithm 178
5.7 Convergence Properties 181
5.8 Concluding Remarks 184
REFERENCES 185
6 IMPLEMENTATION OF INTERIOR POINT
METHODS FOR LARGE SCALE LINEAR
PROGRAMS
Erling D. Andersen, Jacek Gondzio, Csaba Meszdros,
Xiaojie Xu 189
6.1 Introduction 190
6.2 The Primal dual Algorithm 193
6.3 Self dual Embedding 200
6.4 Solving the Newton Equations 204
6.5 Presolve 225
6.6 Higher Order Extensions 230
6.7 Optimal Basis Identification 235
6.8 Interior Point Software 240
6.9 Is All the Work Already Done? 243
6.10 Conclusions 244
REFERENCES 245
Part II CONVEX PROGRAMMING 253
7 INTERIOR POINT METHODS FOR CLASSES
OF CONVEX PROGRAMS
Florian Jarre 255
7.1 The Problem and a Simple Method 256
7.2 Self Concordance 258
7.3 A Basic Algorithm 281
7.4 Some Applications 291
REFERENCES 293
8 COMPLEMENTARITY PROBLEMS
Akiko Yoshise 297
8.1 Introduction 297
8.2 Monotone Linear Complementarity Problems 300
8.3 Newton s Method and the Path of Centers 308
8.4 Two Prototype Algorithms for the Monotone LCP 316
8.5 Computational Complexity of the Algorithms 332
8.6 Further Developments and Extensions 339
8.7 Proofs of Lemmas and Theorems 345
REFERENCES 359
9 SEMIDEFINITE PROGRAMMING
Motakuri V. Ramana, Panos M. Pardalos 369
9.1 Introduction 369
9.2 Geometry and Duality 370
9.3 Algorithms and Complexity 377
9.4 Applications 383
9.5 Concluding Remarks 390
REFERENCES 391
10 IMPLEMENTING BARRIER METHODS FOR
NONLINEAR PROGRAMMING
David F. Shanno, Mark G. Breitfeld, Evangelia M.
Simantiraki 399
10.1 Introduction 399
10.2 Modified Penalty Barrier Methods 402
10.3 A Slack Variable Alternative 407
10.4 Discussion and Preliminary Numerical Results 411
REFERENCES 413
Part III APPLICATIONS, EXTENSIONS 415
11 INTERIOR POINT METHODS FOR
COMBINATORIAL OPTIMIZATION
John E. Mitchell 417
11.1 Introduction 417
11.2 Interior Point Branch and Cut Algorithms 419
11.3 A Potential Function Method 441
11.4 Solving Network Flow Problems 445
11.5 The Multicommodity Network Flow Problem 451
11.6 Computational Complexity Results 455
11.7 Conclusions 457
REFERENCES 459
12 INTERIOR POINT METHODS FOR GLOBAL
OPTIMIZATION
Panos M. Pardalos, Mauricio G.C. Resende 467
12.1 Introduction 467
12.2 Quadratic Programming 468
12.3 Nonconvex Potential Function Minimization 474
12.4 Affine Scaling Algorithm for General Quadratic Programming 486
12.5 A Lower Bounding Technique 490
12.6 Nonconvex Complementarity Problems 493
12.7 Concluding Remarks 497
REFERENCES 497
13 INTERIOR POINT APPROACHES FOR THE
VLSI PLACEMENT PROBLEM
Anthony Vannelli, Andrew Kennings, Paulina Chin 501
13.1 Introduction 501
13.2 A Linear Program Formulation of the Placement Problem 503
13.3 A Quadratic Program Formulation of the MNP Placement Model 509
13.4 Towards Overlap Removal 512
13.5 Primal Dual Quadratic Interior Point Methods 514
13.6 Numerical Results 518
13.7 Conclusions 524
REFERENCES 526
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| classification_rvk | SK 870 |
| ctrlnum | (OCoLC)35084922 (DE-599)BVBBV011195293 |
| dewey-full | 519.7/21 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.7/21 |
| dewey-search | 519.7/21 |
| dewey-sort | 3519.7 221 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011195293 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:05:36Z |
| institution | BVB |
| isbn | 0792342011 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007509170 |
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| physical | XXI, 528 S. graph. Darst. |
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| publisher | Kluwer Acad. Publ. |
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| series | Applied optimization |
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| spelling | Interior point methods of mathematical programming ed. by Tamás Terlaky Dordrecht [u.a.] Kluwer Acad. Publ. 1996 XXI, 528 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied optimization 5 The book provides an overview of the research in interior point methods since the publication of N. Karmarkar's seminal paper in 1984. Leading international experts have contributed to the book with summaries of their relevant areas of specialization. Part I gives an overview of basic variants of interior point algorithms for linear programming. Duality-theory for LP and sensitivity analysis is developed. Results on the affine scale, path following, potential reduction, infeasible interior point methods and implementation strategies are discussed. Part II deals with nonlinear programming. Here necessary smoothness conditions are introduced and illustrated. Algorithms for general smooth convex problems, complementarity and semidefinite optimization problems are presented. The implementation of barrier methods for general nonlinear optimization problems is also considered. Part III covers some application areas such as combinatorial optimization, global optimization and VLSI design. Mathematische programmering gtt Programacao matematica larpcal Programmation (Mathématiques) Programmation linéaire Interior-point methods Linear programming Innere-Punkte-Methode (DE-588)4352322-5 gnd rswk-swf Innere-Punkte-Methode (DE-588)4352322-5 s DE-604 Terlaky, Tamás Sonstige oth Applied optimization 5 (DE-604)BV010841718 5 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007509170&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Interior point methods of mathematical programming Applied optimization Mathematische programmering gtt Programacao matematica larpcal Programmation (Mathématiques) Programmation linéaire Interior-point methods Linear programming Innere-Punkte-Methode (DE-588)4352322-5 gnd |
| subject_GND | (DE-588)4352322-5 |
| title | Interior point methods of mathematical programming |
| title_auth | Interior point methods of mathematical programming |
| title_exact_search | Interior point methods of mathematical programming |
| title_full | Interior point methods of mathematical programming ed. by Tamás Terlaky |
| title_fullStr | Interior point methods of mathematical programming ed. by Tamás Terlaky |
| title_full_unstemmed | Interior point methods of mathematical programming ed. by Tamás Terlaky |
| title_short | Interior point methods of mathematical programming |
| title_sort | interior point methods of mathematical programming |
| topic | Mathematische programmering gtt Programacao matematica larpcal Programmation (Mathématiques) Programmation linéaire Interior-point methods Linear programming Innere-Punkte-Methode (DE-588)4352322-5 gnd |
| topic_facet | Mathematische programmering Programacao matematica Programmation (Mathématiques) Programmation linéaire Interior-point methods Linear programming Innere-Punkte-Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007509170&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT terlakytamas interiorpointmethodsofmathematicalprogramming |